Biomedical Engineering Reference
In-Depth Information
sensor chip surface acts like a Cantor-like dust (
Viscek, 1989
). As the fractal dimension in
the dissociation phase increases by a factor of 2.63 from a value of
D
fd1
equal to 1.0386 to
D
fd2
equal to 2.7294, the dissociation rate coefficient increases by a factor of 16 from a value
of
k
d1
equal to 0.2309 to
k
d2
equal to 3.6949. Changes in the fractal dimension or the degree
of heterogeneity on the sensor chip surface and in the dissociation rate coefficient are in the
same direction.
Figure 14.8b
shows the binding and dissociation of 10 pM SEB in solution to the antibody-
functionalized microbeads on a sensor chip. A single-fractal analysis is adequate to describe
the binding and the dissociation kinetics. The values of (a) the binding rate coefficient,
k
, and
the fractal dimension,
D
f
, for a single-fractal analysis, and (b) the dissociation rate coefficient,
k
d
, and the fractal dimension,
D
fd
, for a single-fractal analysis, are given in
Tables 14.4
and
14.5
.
In this case, the affinity,
K
(
k
/
k
d
), value is 0.0245. No reason is given here to indicate why at
this lower SEB concentration (1 pM) a single-fractal analysis is adequate to describe the binding
and dissociation kinetics, whereas at the higher SEB concentration (1 nM) a dual-fractal analy-
sis is required to describe the binding and the dissociation kinetics. Once again, the zero value
obtained for the fractal dimension,
D
f1
, for a dual-fractal analysis indicates that for this initial
phase of binding the sensor chip surface acts like a Cantor-like dust (
Viscek, 1989
).
ΒΌ
Figure 14.8c
shows the binding and dissociation of 100 fM SEB in solution to the antibody-
functionalized microbeads on a sensor chip. The monoclonal antibody that is specific for
SEB is covalently attached to the silica beads. A dual-fractal analysis is required to describe
the binding and the dissociation kinetics. The values of (a) the binding rate coefficient,
k
, and
the fractal dimension,
D
f
, for a single-fractal analysis, (b) the binding rate coefficients,
k
1
and
k
2
, and the fractal dimensions,
D
f1
and
D
f2
, for a dual-fractal analysis, (c) the dissociation rate
coefficient,
k
d
, and the fractal dimension,
D
fd
, for a single-fractal analysis, and (d) the disso-
ciation rate coefficients,
k
d1
and
k
d2
, and the fractal dimensions,
D
fd1
and
D
fd2
, for a dual-
fractal analysis are given in
Tables 14.6
and
14.7
. In this case, during the initial phase of
dissociation, the estimated value of the fractal dimension,
D
fd1
, is 0. This, once again,
indicates that the sensor chip surface in this phase acts like a Cantor-like dust (
Viscek,
1989
). As the fractal dimension in the binding phase decreases by a factor of 33.85 from a
value of
D
f1
equal to 0.4265 to
D
f2
equal to 0.0126, the binding rate coefficient increases
by a factor of 2.06 from a value of
k
1
equal to 0.0.01438 to
k
2
equal to 0.02969. This is
one of the few cases wherein the changes in the fractal dimension or the degree of heteroge-
neity on the sensor chip surface and in the binding rate coefficient are in the opposite direct-
ions. No reason is given, at present, to explain this.
Figure 14.8d
shows the binding and dissociation of 10 fM SEB in solution to the antibody-
functionalized microbeads on a sensor chip. A single-fractal analysis is adequate to describe the
binding kinetics. A dual-fractal analysis is required to describe the dissociation kinetics. The
values of (a) the binding rate coefficient,
k
, and the fractal dimension,
D
f
, for a single-fractal
